After giving Khan a three-year prison sentence for alleged corruption last week, Humayun Dilawar took a flight to the UK.
The judge is attending East Yorkshire University's human rights and rule of the law training program.
Khan, who was removed from power last year, maintains that the accusations against him were made for political advantage.
On Tuesday, Khan’s followers protested the hosting of the judge they called a "killer of justice" by waving Pakistani flags and banners at the university's Cottingham Road campus.
Others demanded the release of the former prime minister while waving the PTI flag.
The university said it had "no role in the selection" of participants and has been educating Pakistani judges since 2014.
According to a spokesperson, the high courts of Islamabad and Peshawar, as well as the Supreme Court of Pakistan, selected the current cohort for the course, as reported by the Local Democracy Reporting Service.
Khan was convicted on Saturday of failing to disclose the proceeds from the sale of gifts he acquired while in government.
He is prohibited from holding office for five years as a result of his conviction last week.